Algebra Puzzle – Challenge 35
Algebra Puzzle - Challenge 35 is a multiple-choice math challenge from Effortless Math. Read the problem, choose from the answer options below, then open the solution to see the full step-by-step working and check your reasoning against it.
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Challenge:
The ratio of the ages of Eric and Tara is 2 to 3 and the ratio of the ages of Tara and Marshall is 9 to 7. If the sum of their ages is 66, then how old is Eric?
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The correct answer is 18.
Let E be the age of Eric, T be the age of Tara and M be the age of Marshall.
E + T + M = 66
The ratio of E to T is 2 to 3. So:
(E = frac{2}{3} T)
The ratio of T to M is 9 to 7. So:
(M = frac{7}{9} T)
Replace the value of E and M in the first equation with their values in the second and third equations:
(frac{2}{3} T + T + frac{7}{9} T = 66 → frac{22}{9} T = 66 → T = 27)
(E = frac{2}{3} T ⇒ E = frac{2}{3} (27) = 18)
Eric is 18 years old now.
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